A convenience store sold chicken, tuna and bacon sandwiches. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 5 : 7. The ratio of the number of tuna sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some chicken sandwiches and made another 21 tuna sandwiches, there was an equal number of chicken, tuna and bacon sandwiches left. Find the number of chicken sandwiches sold.

	Chicken	Tuna	Bacon	Total
Comparing chicken to total	5x9			7x9
Comparing  tuna to total		1x7		9x7
	45 u	7 u	11 u	63 u

	Chicken	Tuna	Bacon	Total
Before	45 u	7 u	11 u	63 u
Change	- 34 u	+ 21	No change
After	1x11 = 11 u	1x11 = 11 u	1x11 = 11 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 9 and 7 is 63.

Number of bacon sandwiches remains the same at first and in the end. Make the number of bacon sandwiches the  same. LCM of 1 and 11 is 11.

Number of bacon sandwiches 
= 63 u - 45 u - 7 u
= 11 u

Number of chicken, tuna and bacon sandwiches is the same in the end. 

Number of tuna sandwiches = 7 u + 21

7 u + 21 = 11 u
11 u - 7 u = 21
4 u = 21

1 u = 21 ÷ 4 = 2

Number of chicken sandwiches sold
= 45 u - 11 u
= 34 u
= 34 x 2
= 68

Answer(s): 68